High-speed data transmission channels are often subject to severe inter-symbol interference (ISI), due to amplitude distortion in the frequency domain. The accepted solution to this problem is to use a feed-forward equalizer (FFE) together with a decision feedback equalizer (DFE) at the receiver, in order to cancel interference from past signals. One of the problems caused by such a DFE is error propagation, since once an error has been introduced into one of the samples, the DFE will “remember” the error over many subsequent samples.
If the channel impulse response is known, a suitable Tomlinson-Harashima precoder can be used in the transmitter, and can eliminate the need for the DFE in the receiver. Precoders of this sort are described by Wei, for example, in an article entitled, “Generalized Square and Hexagonal Constellations for Intersymbol-Interference Channels with Generalized Tomlinson-Harashima Precoders, ” published in IEEE Transactions on Communications, 42:9 (September 1994), pp. 2713–2721, which is incorporated herein by reference. The precoder in this context is intended to compensate for inter-symbol interference caused by a channel having an equivalent discrete-time response expressed as   1  +            ∑              i        =        1            k        ⁢                  h        i            ⁢                        z                      -            i                          .            
The Tomlinson-Harashima precoder comprises a two-dimensional modulo device with a negative feedback loop. The modulo device takes each complex input symbol that it receives, r, into an output symbol s given by:si=ri−ki·2M  (1)wherein i=1,2, giving the real and imaginary parts of s and r; 2M is the modulo value; and ki is an integer such that −M≦si<M. In the feedback loop, the symbols output by the modulo device are filtered by a digital filter having a discrete time response based on the equivalent discrete-time response of the channel, without the zero-order time-domain component. In other words, the filter response in the feedback loop is given by       ∑          i      =      1        k    ⁢            h      i        ⁢                  z                  -          i                    .      The filtered feedback symbols are subtracted from the modulated symbols (whether coded or uncoded) that are input to the precoder for transmission.
In the receiver, the channel-distorted symbols are input to a modulo device, which is identical to that in the precoder. Assuming that the equalizer's response is well-matched to the actual response of the channel, the symbols output by the modulo device in the receiver will be identical, to within the white Gaussian noise added by the channel, to the modulated symbols that were input to the precoder for transmission. The output symbols can then be processed by a decision device or Viterbi decoder, as appropriate, to recover the input data.
It commonly occurs in communication systems that the channel response and noise characteristics change over time or even in the course of a single communication session between a given receiver and transmitter. If the precoder has a fixed filter response in its feedback loop, it will not be able to compensate for such changes. Therefore, in some communication systems, an adaptive DFE is provided in the receiver, in addition to the precoder in the transmitter. Typically, a known training sequence is transmitted from the transmitter to the receiver, and an adaptation procedure, such as a least-mean-square (LMS) procedure, as is known in the art, is used to adjust the DFE filter coefficients to convergence. Once the DFE coefficients have converged, an indication of the coefficients is sent back to the transmitter for implementation in the feedback loop of the precoder. The DFE can then be deactivated entirely or, alternatively, it may remain active in order to adapt for any subsequent channel variations or noise.
U.S. Pat. Nos. 5,513,216 and 5,604,769, whose disclosures are incorporated herein by reference, describe a hybrid equalizer arrangement of this sort, using a DFE in the receiver in conjunction with a precoder in the transmitter. The DFE includes both an ISI DFE part and a noise-predictive DFE part. Signals received from the transmitter are first processed by a FFE and are then decoded by a Tomlinson-Harashima modulo decoder. The resultant decoded signals are processed by the DFE in conjunction with a slicer in order to recover the transmitted symbols. The ISI DFE coefficients are conveyed back for implementation in the precoder. The noise-predictive part of the DFE may remain active or, alternatively, the noise-predictive coefficients may be implemented in the precoder, as well. Assuming the adapted ISI DFE response to be I(z), and the noise-predictive DFE response to be N(z), the filter response in the feedback loop of the precoder is set to be C(z)=[1+I(z)]·[1+N(Z)]−1. When variations occur in the channel characteristics, new coefficients may be determined at the DFE in a “quick retrain” procedure. These coefficients can then be conveyed back to the transmitter for implementation in the precoder.